2x^2+2x=-8x-12

Solution for 2x^2+2x=-8x-12 equation:

Simplifying
2x2 + 2x = -8x + -12

Reorder the terms:
2x + 2x2 = -8x + -12

Reorder the terms:
2x + 2x2 = -12 + -8x

Solving
2x + 2x2 = -12 + -8x

Solving for variable 'x'.

Reorder the terms:
12 + 2x + 8x + 2x2 = -12 + -8x + 12 + 8x

Combine like terms: 2x + 8x = 10x
12 + 10x + 2x2 = -12 + -8x + 12 + 8x

Reorder the terms:
12 + 10x + 2x2 = -12 + 12 + -8x + 8x

Combine like terms: -12 + 12 = 0
12 + 10x + 2x2 = 0 + -8x + 8x
12 + 10x + 2x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
12 + 10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5x + x2) = 0

Factor a trinomial.
2((3 + x)(2 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-3, -2}